Finance

The discipline has two main areas of focus:See the discussion re finance theory by Fama and Miller under {{section link||Notes}}. [[asset pricing]] and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:

The discipline has two main areas of focus:See the discussion re finance theory by Fama and Miller under {{section link||Notes}}. [[asset pricing]] and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:

# Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the [[outline of finance#Portfolio theory|portfolio-]] and [[investment theory]] applied in asset management. The analysis essentially explores how [[homo economicus|rational investors]] would apply [[risk-return spectrum|risk and return]] to the problem of [[investment]] under uncertainty, producing the key "[[Fundamental theorem of asset pricing]]". Here, the twin assumptions of [[rational pricing|rationality]] and [[efficient-market hypothesis|market efficiency]] lead to [[modern portfolio theory]] (the [[Capital asset pricing model|CAPM]]), and to the [[Black–Scholes model|Black–Scholes]] theory for [[Valuation of options|option valuation]]. At more advanced levels—and often in response to [[financial crisis|financial crises]]—the study [[Financial economics#Extensions|then extends]] these [[Neoclassical economics#Rational Behavior Assumptions|"neoclassical" models]] to incorporate phenomena where their assumptions do not hold, or to more general settings.

# Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the [[outline of finance#Portfolio theory|portfolio-]] and [[investment theory]] applied in asset management. The analysis essentially explores how [[homo economicus|rational investors]] would apply [[risk-return spectrum|risk and return]] to the problem of [[investment]] under uncertainty, producing the key "[[Fundamental theorem of asset pricing]]". Here, the twin assumptions of [[rational pricing|rationality]] and [[efficient-market hypothesis|market efficiency]] lead to [[modern portfolio theory]] (the [[Capital asset pricing model|CAPM]]), and to the [[Black–Scholes model|Black–Scholes]] theory for [[Valuation of options|option valuation]]. At more advanced levels—and often in response to [[financial crisis|financial crises]]—the study [[Financial economics#Extensions|then extends]] these [[Neoclassical economics#Rational Behavior Assumptions|"neoclassical" models]] to incorporate phenomena where their assumptions do not hold, or to more general settings.

# Much of [[Outline of finance#Corporate finance theory|corporate finance theory]], by contrast, considers investment under "[[certainty]]" ([[Fisher separation theorem]], [[The Theory of Investment Value|"theory of investment value"]], and [[Modigliani–Miller theorem]]). Here, theory and methods are developed for the decisioning about funding, dividends, and capital structure discussed above. A recent development is [[Financial economics#Corporate finance theory|to incorporate uncertainty]] and [[contingent claim valuation|contingency]]—and thus various elements of asset pricing—into these decisions, employing for example [[real options analysis]].

# Much of [[Outline of finance#Corporate finance theory|corporate finance theory]], by contrast, considers investment under "[[certainty]]" ([[Fisher separation theorem]], [[The Theory of Investment Value|"theory of investment value"]], and [[Modigliani–Miller theorem]]). Here, theory and methods are developed for the decisions about funding, dividends, and capital structure discussed above. A recent development is [[Financial economics#Corporate finance theory|to incorporate uncertainty]] and [[contingent claim valuation|contingency]]—and thus various elements of asset pricing—into these decisions, employing for example [[real options analysis]].

===Financial mathematics===

===Financial mathematics===